I am wondering how to proceed, better ask the team to do it or better to apply internally to other team located in the US and put that infront.
Talk to the hiring manager in the US. It will help if that manager knows you are a worthy candidate and would be willing to hire you into his/her team or if some one from their team can vouch for you. Nothing will happen unless the manager in the US team has a position to fill and you are a right fit for that.
In some cases, just ask if they would consider you for the role, if they do then it means that they are ready to sponsor you for L1. You can start by speaking to your manager then applying for the role either through the hiring manager or hr. During the evaluation/recr proc be sure to talk about your future after visa sponsorship and the possibility of the company petitioning for a green card on your behalf once you get to the states.
Well in most of the cases, team don't do Visa transfers anyways. So you should probably get transfer approval from a new team and then the immigration team will take care of the visa formalities.